Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/137

We may place the deflecting magnet with its axis pointing north, at a distance $r$ from the centre of the suspended magnet, the line $r$ making an angle whose cosine is ${\sqrt {\tfrac {1}{3}}}$ with the magnetic meridian. The action of the deflecting magnet on the suspended one is then at right angles to its own direction, and is equal to

$R={\sqrt {2}}{\frac {M}{r^{3}}}$

Here $M$ is the magnetic moment when the axis points north, as in the experiment of vibration, so that no correction has to be made for induction.

This method, however, is extremely difficult, owing to the large errors which would be introduced by a slight displacement of the deflecting magnet, and as the correction by reversing the deflecting magnet is not applicable here, this method is not to be followed except when the object is to determine the coefficient of induction.

The following method, in which the magnet while vibrating is freed from the inductive action of terrestrial magnetism, is due to Dr. J. P. Joule.^[1]

Two magnets are prepared whose magnetic moments are as nearly equal as possible. In the deflexion experiments these magnets are used separately, or they may be placed simultaneously on opposite sides of the suspended magnet to produce a greater deflexion. In these experiments the inductive force of terrestrial magnetism is transverse to the axis.

Let one of these magnets be suspended, and let the other be placed parallel to it with its centre exactly below that of the suspended magnet, and with its axis in the same direction. The force which the fixed magnet exerts on the suspended one is in the opposite direction from that of terrestrial magnetism. If the fixed magnet be gradually brought nearer to the suspended one the time of vibration will increase, till at a certain point the equilibrium will cease to be stable, and beyond this point the suspended magnet will make oscillations in the reverse position. By experimenting in this way a position of the fixed magnet is found at which it exactly neutralizes the effect of terrestrial magnetism on the suspended one. The two magnets are fastened together so as to be parallel, with their axes turned the same way, and at the distance just found by experiment. They are then suspended in the usual way and made to vibrate together through small arcs.

1. Proc. Phil. S., Manchester, March 19, 1867.